A New Multiplicity Formula for the Weyl Modules of Type $B$ and $C$

Abstract:

      A monomial basis and a filtration of subalgebras for the universal enveloping algebra $\U(\g_l)$ of a complex simple Lie algebra $\frak g_l$ of type $B_l$ and $C_l$ are given, and the decomposition of the Weyl module $V(\la)$ as a $\U(\g_l)$-module into a direct sum of Weyl modules $V(\mu)$'s as $\U(\g_{l-1})$-modules is described. In particular, a new multiplicity formula for the Weyl module $V(\la)$ is obtained in this note.